Proposition 1 [1]}
If \(\lambda >0\)  and \(0<m_1<m_2<\infty \) , the following relations hold:
\(\bigg (H_{m_1^+}^{\lambda }\bigg (\log \frac{\gamma }{m_1}\bigg )^{\beta -1}\bigg )(x)=\frac{\Gamma (\beta )}{\Gamma (\beta +\lambda )}\bigg (\log \frac{x}{m_1}\bigg )^{\beta +\lambda -1}\) 
